Solves the generalized least squares problem.
glssoln(a, x, v, tol = sqrt(.Machine$double.eps))glssoln returns a list of two named components:
coeff is \(y\) as above.
residuals is \(e\) as above.
Given matrices \(a\), \(x\), \(v\), glssoln computes \(y\) such that
$$(x-ay)^T v^{-1} (x-ay)$$
is minimized.
This is accomplished by first computing the Choleski decomposition of \(v\):
$$v=LL^T.$$
One then solves for \(y\) in the equation
$$L^{-1}ay=L^{-1}x.$$
This is accomplished by means of a singular-value decomposition of \(L^{-1} a\).
The resulting \(y\) then satisfies $$x=ay+e,$$ where the entries of \(e\) are the residuals.